关于前馈多层神经网络多维函数逼近能力的一个定理

本文首次证明了前馈神经网络多维函数逼近能力的一个重要定理，当隐层神经数目足够多时，其多维函数逼近能力与维数无关，也就是说我们只需研究其一维函数逼近能力，所得的结论完全适合于多维情形，该定量大大简化了前馈多层神经网络函数逼近问题的分析难度，本文还给出了该定理的一个应用。     

基于径向基函数神经网络的CDMA多用户检测方法

径向基函数神经网络是一种三层前馈性神经网络,它具有较强函数逼近能力和分类能力,学习速度快等优点.本文根据径向基函数神经网络的这些优点提出了一种基于径向基函数网络的CDMA多用户检测方法(RMD).计算机模拟表明我们所提的算法具有能克服多址干扰,抑制噪声干扰和对"远-近"问题不敏感等优点,这为研究CDMA多用户检测器开辟了一条新的途径。     

多层前馈网络在模式识别中的理论和应用

本文从理论上证明了具有线性输出单元的多层前馈网络能用作最优特征提取器。同时还证明了多层前馈网络分类器的输出函数是最小均方误差意义下对Ｂａｙｅｓ决策函数的逼近，对于具有线性输出单元的三层前馈网络，当隐层单元数足够多时，这种逼近能达到任意精度。在此基础上，我们提出了一个综合了特征提取网络和分类器网络的组合神经网络模型，其性能好于单个的三层前馈网络。     

可规划相位FIR滤波器的神经网络设计方法

本文针对可规划相频响应的实系数FIR滤波器的逼近问题,采用一个三层复激活函数前馈神经网络来实现。该网络隐层各神经元的激活函数为复指数函数,将滤波器系数作为隐层各神经元到输出层的连接权值,通过对误差函数的最小化来调整权值,并根据网络特性与所要设计的滤波器的特点,提出了一些实际设计中训练样本集选取与误差加权值设置的规则。依托所采用的神经网络,根据上述规则,进行了两例可规划相频特性的实系数FIR滤波器的设计,结果表明所设计滤波器的相频响应较好地满足了设计要求。     

基于径向基函数神经网络的模拟/混合电路故障诊断

径向基函数神经网络是一种前馈型神经网络,具有较强的函数逼近能力和分类能力,学习速度快等优点.本文采用幅值恒定的正弦信号源进行模拟电路的故障仿真,从频域提取输出信号波形的特征值建立故障字典,应用径向基函数神经网络的这些优点进行响应分析和故障诊断,能够实现快速故障诊断及定位,具有准确率高的特点.     

基于BP神经网络-Monte Carlo法的结构可靠性分析

提出通过人工神经网络拟合极限状态函数的方法来解决结构可靠性问题。根据多层神经网络映射存在定理,对于任何在闭区间内的一个连续函数都可以用含有一个隐含层的BP网络来逼近。应用此定理,通过人工神经网络拟合极限状态方程,借助神经网络的函数映射关系产生大量的极限状态函数值,作为下一步的分析数据。此过程并不像Monte Carlo法时每一点都做确定性计算,因而达到减少计算工作量的目的。该方法仅采用Monte Carlo法随机抽样的思路,对大范围的数据进行概率分析,通过概率分析得到极限状态函数值的均值和标准差,以便求得结构系统的可靠性指标,进行结构系统可靠性分析。     

基于MATLAB神经网络工具箱的BP网络设计

本文介绍了MATLAB神经网络工具箱及其常用的工具箱函数;在说明BP网络的模型结构和算法的基础上,讨论了BP网络的训练过程及其设计原则,并用一个典型的两层结构的神经网络实现了具有函数逼近功能的BP网络设计.     

一种新的量子神经网络训练算法

量子神经网络是一种借鉴量子理论中的态叠加思想而设计的单隐层前馈神经网络,其主要用于数据分类。由于采用多层激励函数神经元,并且在量子间隔训练中采用了新的目标函数,即同类输入数据的隐层节点输出方差最小,从而使量子神经网络具备了发掘不同类别数据间模糊性的能力。但由于训练时对量子神经网络权值和量子间隔使用了不同的目标函数,使迭代过程中两者不可避免的会出现相互冲突,从而导致训练迭代次数的增加和网络性能的下降。本文借鉴约束优化理论,在两个目标函数的梯度下降求解中引入了惩罚函数,提出了一种新的量子神经网络训练算法,消除了两个目标函数间的冲突。实验结果表明,本文提出的训练算法可以显著提升训练的速度和网络的性能。      

BP神经网络在函数逼近中的应用研究

函数逼近在纯数学领域、工程和物理学领域得到了广泛的应用。利用人工神经网络映射能力,通过样本不断学习实现对未知函数的逼近。利用BP神经网络研究人工神经网络在函数逼近中的应用,研究过程利用MATLAB神经网络工具箱设计网络并进行仿真实验。     

基于改进的小波神经网络的汽车电控汽油机故障诊断

针对现有BP网络在汽车电控汽油机故障诊断中存在的问题,提出将小波函数与神经网络结合构成小波网络,代替BP网络用于故障诊断。并对小波神经网络提出了两个方面的改进。首先是对输出层函数进行了改进,其次是用熵函数代替均方误差函数作为网络的代价函数。仿真结果表明此改进的小波神经网络算法进行汽车电控汽油机的故障是有效的,而且与传统的BP神经网络相比,该改进的小波神经网络具有更强的逼近能力,更快的网络学习收敛速度和能有效避免局部最小值问题。     

理想导体目标重建的Fourier衍射定理

本文给出推广的物理光学近似下理想导体目标的Ｆｏｕｒｉｅｒ衍射定理，其形式与介质目标的相应关系式十分相似，利用这一关系式可以由测量直线上散射场分布重建二维理想导体目标Ｆｏｕｒｉｅｒ域的空间谱值。通过简单例子讨论了这一关系式的适用性。     

Resource Sharing for Book-Ahead and Instantaneous-Request Calls Using a CLT Approximation

This paper extends the admission control algorithm for book-ahead and instantaneous-request calls proposed by Greenberg, Srikant and Whitt (1997) to cover multiple classes of instantaneous-request calls, each with their own traffic characteristics and their own performance requirements. As before, book-ahead calls specify their starting and finishing times, and are assumed to book far ahead relative to the holding times of the instantaneous-request calls. The book-ahead calls may be constrained by an upper-limit on the capacity that can be reserved for them. Instantaneous-request calls are admitted if the probability of interruption (or some other form of service degradation in response to the conflict) for that call is below a threshold, but now this threshold can be class-dependent, and now the interrupt probability is calculated by a normal approximation based on the central limit theorem. Simulation experiments show that the normal approximation performs as well as the previous detailed calculation in single-class examples, and that the normal approximation can be applied to multi-class examples.     

一种新的混沌扩频序列产生方法

本文提出了一种新的混沌扩频序列产生方法。该方法基于神经网络的强大学习能力和副近非线性函数能力,应用具有全局最优的ＢＰ改进算法通过训练学习建立起具有混沌性态的优化神经网络模型,利用网络权值调整的灵活性来产生混沌扩频序列。计算机仿真结果表明,该模型产生的混沌扩频序列调整更容易,比基于单一混沌映射能产生更多符合扩频通信要求的扩频序列。     

Modular design and implementation of field-programmable-gate-array-based Gaussian noise generator

The modular design of a Gaussian noise generator (GNG) based on field-programmable gate array (FPGA) technology was studied. A new range reduction architecture was included in a series of elementary function evaluation modules and was integrated into the GNG system. The approximation and quantisation errors for the square root module with a first polynomial approximation were high; therefore, we used the central limit theorem (CLT) to improve the noise quality. This resulted in an output rate of one sample per clock cycle. We subsequently applied Newton's method for the square root module, thus eliminating the need for the use of the CLT because applying the CLT resulted in an output rate of two samples per clock cycle (>200 million samples per second). Two statistical tests confirmed that our GNG is of high quality. Furthermore, the range reduction, which is used to solve a limited interval of the function approximation algorithms of the System Generator platform using Xilinx FPGAs, appeared to have a higher numerical accuracy, was operated at >350 MHz, and can be suitably applied for any function evaluation.     

一类反馈神经网络对非线性连续系统近似能力的证明

本文从多层前馈神经网络的一般近似定理出发,证明了带有输入的非线性连续系统在有限时间段内的输出轨迹可以被一类反馈神经网络输出神经元的状态向量近似到任何程度.     

Interpolation revisited

Based on the theory of approximation, this paper presents a unified analysis of interpolation and resampling techniques. An important issue is the choice of adequate basis functions. We show that, contrary to the common belief, those that perform best are not interpolating. By opposition to traditional interpolation, we call their use generalized interpolation; they involve a prefiltering step when correctly applied. We explain why the approximation order inherent in any basis function is important to limit interpolation artifacts. The decomposition theorem states that any basis function endowed with approximation order can be expressed as the convolution of a B-spline of the same order with another function that has none. This motivates the use of splines and spline-based functions as a tunable way to keep artifacts in check without any significant cost penalty. We discuss implementation and performance issues, and we provide experimental evidence to support our claims.     

带阶梯输出函数的细胞神经网络

本文给出了带阶梯输出函数的细胞神经网络的稳定性定理。利用阶梯输出函数的各“台阶”记忆不同灰度，实现了灰度模式的ＣＮＮ联想记忆。     

A general sampling theory for nonideal acquisition devices

The authors first describe the general class of approximation spaces generated by translation of a function ψ(x), and provide a full characterization of their basis functions. They then present a general sampling theorem for computing the approximation of signals in these subspaces based on a simple consistency principle. The theory puts no restrictions on the system input which can be an arbitrary finite energy signal; bandlimitedness is not required. In contrast to previous approaches, this formulation allows for an independent specification of the sampling (analysis) and approximation (synthesis) spaces. In particular, when both spaces are identical, the theorem provides a simple procedure for obtaining the least squares approximation of a signal. They discuss the properties of this new sampling procedure and present some examples of applications involving bandlimited, and polynomial spline signal representations. They also define a spectral coherence function that measures the “similarity” between the sampling and approximation spaces, and derive a relative performance bound for the comparison with the least squares solution     

Design of 2-D FIR Filters by a Feedback Neural Network

A Hopfield-type neural network for the design of 2-D FIR filters is proposed. The network is contrived to have an energy function that coincides with the sum-squared error of the approximation problem at hand and by ensuring that the energy is a monotonic decreasing function of time, the approximation problem can be solved. Two solutions are obtained. In the first the 2-D FIR filter is designed on the basis of a specified amplitude response and in the second a filter that has specified maximum passband and stopband errors is designed. The network has been simulated with HSPICE and design examples are included to show that this is an efficient way of solving the approximation problem for 2-D FIR filters. The neural network has high potential for implementation in analog VLSI and can, as a consequence, be used in real-time applications.     

Numerical Determination of Potential in Inhomogeneous Dielectrics by Earnshaw's Theorem

Earnshaw's theorem, a characterization of potential functions equivalent to Poisson's equation, expresses a relation between the value of the potential at a point and an average of the function over a spherical surface centered at the point. The theorem therefore lends itself to use in numerical computation of the potential. A formulation of the theorem is presented with particular reference to determination of the potential in a region which is inhomogeneously occupied by dielectric media. This provides a rigorous basis for the formulas used to determine the potential at points on a dielectric interface, in that it avoids the ambiguity which arises in the evaluation of the finite-difference approximation to the Laplacian at such points. The use of the formulation is illustrated by examples of computer-generated graphs giving the potential in the presence of irregular dielectric objects.